AVHRR is an imager flying on polar meteorological satellites that, due to its spatial resolution (about 1 km at Nadir view),
produces a huge amount of data. A method based on the wavelet packet transform is devised to compress AVHRR images. The
method is driven by the compression error (application dependent), so that different types of images have the same quality. The
best basis wavelet packet is chosen by L1
norm criterion that was found to be the most suited for the problem at hand. Ability of
the compression method to preserve most fine structures of the images even at the highest resolution is demonstrated based on
some examples. Comparison with wavelet algorithms is performed.
Let $q>1$. Initiated by P. Erd\H os et al. in \cite{ErdJooKom1}, several authors
studied the numbers $l^m(q)=\inf \{y\ :\ y\in\Lambda_m,\ y\ne 0\}$,
$m=1,2,\dots$, where $\Lambda_m$ denotes the set of all finite sums of the form
$y=\eps_0 + \eps_1 q + \eps_2 q^2 + \dots + \eps_n q^n$
with integer coefficients $-m\le \eps_i \le m$. It is
known (\cite{Bug}, \cite{ErdJooKom1}, \cite{ErdKom}) that $q$ is a Pisot number
if and only if $l^m(q)>0$ for all $m$. The value of $l^1(q)$ was determined for
many particular Pisot numbers, but the general case remains widely open. In this
paper we determine the value of $l^m(q)$ in other cases.
The phase-separation kinetics of binary fluids in shear flow is studied numerically in the framework of the continuum convection-diffusion equation based on a Ginzburg-Landau free energy. Simulations are carried out for different temperatures both in d=2 and 3. Our results confirm the qualitative picture put forward by the large-Rr limit equations studied by Corberi et al. [Phys. Rev. Lett. 81, 3852 (1998)]. In particular, the structure factor is characterized by the presence of four peaks whose relative oscillations give rise to a periodic modulation of the behavior of the rheological indicators and of the average domains sizes. This peculiar pattern of the structure factor corresponds to the presence of domains with two characteristic thicknesses, whose relative abundance changes with time.
Results are presented for the phase separation process of a binary mixture subject to a uniform shear flow quenched from a disordered to a homogeneous ordered phase. The kinetics of the process is described in the context of the time-dependent Ginzburg-Landau equation with an external velocity term. The large-n approximation is used to study the evolution of the model in the presence of a stationary flow and in the case of an oscillating shear. For stationary flow we show that the structure factor obeys a generalized dynamical scaling. The domains grow with different typical length scales R-x and R-perpendicular to, respectively, in the flow direction and perpendicularly to it. In the scaling regime R(perpendicular to)similar to t(alpha perpendicular to) and R(x)similar to gamma(alpha x) (with logarithmic corrections), gamma being the shear rate, with alpha(x)=5/4 and alpha(perpendicular to)=1/4. The excess viscosity Delta eta after reaching a maximum relaxes to zero as gamma(-2)t(-3/2). Delta eta and other observables exhibit logarithmic-time periodic oscillations which can be interpreted as due to a growth mechanism where stretching and breakup of domains occur cyclically. In the case of an oscillating shear a crossover phenomenon is observed: Initially the evolution is characterized by the same growth exponents as for a stationary flow. For longer times the phase-separating structure cannot align with the oscillating drift and a different regime is entered with an isotropic growth and the same exponents as in the case without shear.
The effect of shear flow on the phase-ordering dynamics of a binary mixture with field-dependent mobility is investigated. The problem is addressed in the context of the time-dependent Ginzburg-Landau equation with an external velocity term, studied in self-consistent approximation. Assuming a scaling ansatz for the structure factor, the asymptotic behavior of the observables in the scaling regime can be analytically calculated. All the observables show log-time periodic oscillations which we interpret as due to a cyclical mechanism of stretching and break-up of domains. These oscillations are damped as consequence of the vanishing of the mobility in the bulk phase.
